Question: Solve for $x$, $ -\dfrac{8}{20x} = \dfrac{x - 6}{5x} + \dfrac{4}{20x} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $20x$ $5x$ and $20x$ The common denominator is $20x$ The denominator of the first term is already $20x$ , so we don't need to change it. To get $20x$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{x - 6}{5x} \times \dfrac{4}{4} = \dfrac{4x - 24}{20x} $ The denominator of the third term is already $20x$ , so we don't need to change it. This give us: $ -\dfrac{8}{20x} = \dfrac{4x - 24}{20x} + \dfrac{4}{20x} $ If we multiply both sides of the equation by $20x$ , we get: $ -8 = 4x - 24 + 4$ $ -8 = 4x - 20$ $ 12 = 4x $ $ x = 3$